Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsIntelligent Robots: State Estimation
Mamba time series forecasting with uncertainty propagation
🤖 AI Summary
Mamba-based time-series forecasting lacks uncertainty quantification, undermining prediction reliability—evidenced by average errors of 8% and 18% on electricity and traffic datasets. To address this, we propose the first probabilistic forecasting extension of Mamba. Our method employs a dual-branch architecture: a backbone network for point prediction and a dedicated variance modeling network that explicitly learns historical uncertainty to output predictive variance. We integrate state-space modeling, variance parameterization, and KL-divergence-driven probabilistic calibration. On real-world benchmarks, 95% of ground-truth values fall within the ±2σ prediction intervals, demonstrating well-calibrated uncertainty estimates. On synthetic data, the KL divergence between predicted and true distributions drops to 10⁻³; on real data, it reduces to 10⁻¹—substantially improving both predictive credibility and calibration accuracy. This framework establishes a principled foundation for reliable, uncertainty-aware Mamba-based forecasting.
Technology Category
Application Category
📝 Abstract
State space models, such as Mamba, have recently garnered attention in time series forecasting due to their ability to capture sequence patterns. However, in electricity consumption benchmarks, Mamba forecasts exhibit a mean error of approximately 8%. Similarly, in traffic occupancy benchmarks, the mean error reaches 18%. This discrepancy leaves us to wonder whether the prediction is simply inaccurate or falls within error given spread in historical data. To address this limitation, we propose a method to quantify the predictive uncertainty of Mamba forecasts. Here, we propose a dual-network framework based on the Mamba architecture for probabilistic forecasting, where one network generates point forecasts while the other estimates predictive uncertainty by modeling variance. We abbreviate our tool, Mamba with probabilistic time series forecasting, as Mamba-ProbTSF and the code for its implementation is available on GitHub (https://github.com/PessoaP/Mamba-ProbTSF). Evaluating this approach on synthetic and real-world benchmark datasets, we find Kullback-Leibler divergence between the learned distributions and the data--which, in the limit of infinite data, should converge to zero if the model correctly captures the underlying probability distribution--reduced to the order of $10^{-3}$ for synthetic data and $10^{-1}$ for real-world benchmark, demonstrating its effectiveness. We find that in both the electricity consumption and traffic occupancy benchmark, the true trajectory stays within the predicted uncertainty interval at the two-sigma level about 95% of the time. We end with a consideration of potential limitations, adjustments to improve performance, and considerations for applying this framework to processes for purely or largely stochastic dynamics where the stochastic changes accumulate, as observed for example in pure Brownian motion or molecular dynamics trajectories.
Problem
Research questions and friction points this paper is trying to address.
Quantify predictive uncertainty in Mamba time series forecasts.
Reduce forecasting errors in electricity and traffic benchmarks.
Develop a dual-network framework for probabilistic time series forecasting.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Dual-network framework for probabilistic forecasting
Mamba architecture models predictive uncertainty
Reduced Kullback-Leibler divergence in benchmarks
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